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Simplifying 0 = 135 + -6t + -1t2 Solving 0 = 135 + -6t + -1t2 Solving for variable 't'. Combine like terms: 0 + -135 = -135 -135 + 6t + t2 = 135 + -6t + -1t2 + -135 + 6t + t2 Reorder the terms: -135 + 6t + t2 = 135 + -135 + -6t + 6t + -1t2 + t2 Combine like terms: 135 + -135 = 0 -135 + 6t + t2 = 0 + -6t + 6t + -1t2 + t2 -135 + 6t + t2 = -6t + 6t + -1t2 + t2 Combine like terms: -6t + 6t = 0 -135 + 6t + t2 = 0 + -1t2 + t2 -135 + 6t + t2 = -1t2 + t2 Combine like terms: -1t2 + t2 = 0 -135 + 6t + t2 = 0 Factor a trinomial. (-15 + -1t)(9 + -1t) = 0Subproblem 1
Set the factor '(-15 + -1t)' equal to zero and attempt to solve: Simplifying -15 + -1t = 0 Solving -15 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + -1t = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -1t = 0 + 15 -1t = 0 + 15 Combine like terms: 0 + 15 = 15 -1t = 15 Divide each side by '-1'. t = -15 Simplifying t = -15Subproblem 2
Set the factor '(9 + -1t)' equal to zero and attempt to solve: Simplifying 9 + -1t = 0 Solving 9 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1t = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1t = 0 + -9 -1t = 0 + -9 Combine like terms: 0 + -9 = -9 -1t = -9 Divide each side by '-1'. t = 9 Simplifying t = 9Solution
t = {-15, 9}
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